Executive summary of the charges: they were being a human roadblock, they were being loud, and they were preventing third parties from using the space in which they were protesting. Doubtless these people were also dressed like hippies, which was not a crime on the books at the time, but which probably contributed to their arrest. The big sticking point of the petition before the Supreme Court was that when the police arrived, the crowd was small and calm, and the very act of the police trying to disperse them caused them to become unruly. I'll quote again--note that the word "horses" means "police on horseback":

The evidence showed that the meeting was peaceful and orderly until the horses arrived. Up to that time the crowd was apparently small with no one paying much attention. The bulk of the evidence at the trial related to acts of individual petitioners during the period when the police were trying to disperse the crowd, that is, between the advent of the horses and the arrests.

They were arrested for disturbing the peace, but they were tried based on the disturbance they caused once the police tried to disperse them. Since those actions occurred after the original charge, they could not have been part of that charge, and so any conviction on the original charge cannot be based on the actions after that charge. To quote, much more succinctly, the Court's opinion,

"A conviction on one ground may not be sustained on grounds that might have been charged but were not... Where First Amendment rights are involved, as they were here, we have been meticulous to insist upon clean-cut violations of ordinances protecting law and order, lest broad
or fuzzy applications be used to suffocate or impair the exercise of those constitutional rights."